4th ANSA & μETA International Conference
CFD ANALYSIS OF WINDSHIELD HEATER SYSTEM
1
Wei Liu, 2Haijun Jia
Beijing FEAonline Engineering Co.,Ltd. Beijing, China
Keywords: windshield, finite element method, heat transfer
Abstract：Understanding the heat transfer interaction between inflow fluids and windshield
surface is of ramount practical significance. In this paper, the heat transfer process is
investigated utilizing a three-dimensional finite element method. Numerical analyses using
Ansa and Thesues predict a detailed description of heat transfer. The answer shows the
simulation method is feasible and convenient
1 Introduction
Windshield is an important accessory to a car. With the progress in large curvature,
hyperboloid, large spherical flat of windshield, trial and error method has been unable to
[1, 2 ]
meet the needs of development for new product. Therefore, the further research
of
windshield hot-bend and tempering forming process, which combined with finite element
numerical simulation technology, established a comprehensive numerical model, has the
important theoretical significance and practical value. This paper deals with the numerical
simulation analysis of windshield forming, and puts forward a usefull method for windshield
design. Based on the 3D transient heat conduction theory, the mathematical models of
windshield simulation are set up.With the instance of the windshield, the numerical simulation
analysis of the transient temperature field has completed with finite element analysis
software—THESUES and ANSA. In differente time, the distributions of the temperature of
the windshield are gotten. The simulation result can be concluded that the simulation answer
is acceptable and reliable.Finally, the paper summarizes windshield surface design ideas,
which provides a reference for the processing technology of the windshield.
2 Question describe:
Figure 1 shows the geometry model of the winshield, the air flows from the winshield outside
to winshield surfaces , the blue lines means the blowing grid.
The inlet air pressure near side 1 surface is 20Kpa, air temprature is 293K. The inlet air
pressure near side 2 surface is 17Kpa, air temprature is 293K. Initial time, the windshield
temperature is 923K. Blowing time is 15 second.
4th ANSA & μETA International Conference
Fig. 1 The geometry model
3 Numerical method:
3.1 Theory about the windshield heat transfer analys
3
For each material point in a solid regine, according the law of conservation of energy, the
time rate of change of the total enegy is equal to the change of heat content per unit time.
ρc
∂T
= −∇q + Q
∂t
(1)
3
If working forces are not considered. Here, ρ denotes the density[ kg / m ], T the
o
2
temperature[ C ], c the specific heat[ J /(kgK ) ], q the conductive heat flux vector [ W / m ],
3
and Q the internal heat generation[ W / m ]. Fourier’s heat conduction law states:
q = − k ⋅ ∇T
(2)
x=xe
i i we get the
In terms of the conductivity tensor K. for a cartesian coordinate system
following differential equation for the unknown temperature distribution in a solid region Ω :
ρc
∂T
∂
∂T
=
(k ij
)+Q
∂t ∂x i
∂x j
(3)
k ij
are components of the symmetric conductivity tensor. The indices i,j=1,2,3 represent the
three coordinates. On the boundary region, for the windshield heat system, neglect the
radiation from windshield, the energy conservation law leads to:
− (k ij
∂T
)ni = q bc = −q conv
∂x j
(4)
4th ANSA & μETA International Conference
The boundary heat fluxes
function of a position
q bc [W / m 2 ] consists of the convective q conv . These heat fluxes are
s = ( s1 , s 2 , s 3 ) on the boundary and the time t. See figure 2.
Fig.2 Solid structure with boundary conditions
3.2 Finite Element Approach
A so called weak form of (2) and (3) over a finite element is obtained by multipling (2) with a
weight function w(x ) .The integral representation of the energy conservation law is follow:
∂T
∫ w[(ρc ∂t
− Q) + k ij
Ωe
∂w ∂T
]dx − ∫ w(∑ q bc )ds = 0
∂x i ∂x j
Γe
(5)
By the interpolation, the so-called weak-form of the finite element model is obtained:
∑ (M
e
ij
T je + K ije T je ) − Qie − q ie = 0
(6)
T je =
∂T je
∂t
(7)
The details of (6) shows in reference[2].
3.3 Mesh generation
The hexa meshing is generated by ANSA, see figure3.
4th ANSA & μETA International Conference
Surface grid
Inner grid
Fig 3 mesh
3.4 Analys method
The boundary condition:
Pside1 = 20 KPa ,
4th ANSA & μETA International Conference
Tside1 = 20 o C ,
Pside 2 = 17 KPa ,
Tside 2 = 20 o C .
Initial contition:
t = 0s ,
Twindshield = 600o C ,
Material:
glass
Solver method:
Unsteady flow,
t = 0,1,2,...,15 s
The convection coefficient between the air and the windshield is shown in fig4:
Fig4 surface convection coefficient
3.5 Result
Figure 5 shows the windshield surface temperature distribution in differente time, when t=0s,
o
o
the suface temperature is 600 C ; when t=15s, the max temperature become 130 C , the
o
min temperature become 49 C . These means that the windshield’s temperature has fallen
o
by 500 C (at least) in 15 seconds.
The same conclusion can be tested in Figure6, these also show the process of heat transfer
inside the windshield.
4th ANSA & μETA International Conference
Figure 7 is the average temperature distribution in differente time, we can see that the
o
average temperature has fallen by 525 C in 15 seconds.
T=0s
T=1s
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T=5s
T=7s
4th ANSA & μETA International Conference
T=10s
T=15s
Fig.5 temperature distribution on surface
4th ANSA & μETA International Conference
T=0s
T=5s
4th ANSA & μETA International Conference
T=10s
T=15
Fig.6 temperature distribution inside the windshield
4th ANSA & μETA International Conference
Fig.7 average temperature distribution
4 Conclusion
The analys model of unsteady temperature field about the windshield is established by Ansa
and Thesues, the results shows the windshield temperature distribution with differente time.
the temperature fall rapidly in 15 seconds, these are good correspond to reality. The
simulative way will make the processing technology of the windshield more feasible and
convenient.
Reference
[1] AbdulNour, B. S., and Foss, J. F., 1997, “Computational and Experimental Predictions of
Automotive Windshield Flow”, Proceedings of ASME Fluids Engineering Division Summer.
Meeting; ASME Paper No. FEDSM97-3022
[2] Nasr, K.J. and AbdulNour. B.S. (2000) ‘Defrosting of Automotive Windshields: Progress
and Challenges’, Int. J. of Vehicle Design. Vol. 23. Nos. 3/4, pp. 360-375.
[3] AbdulNour, R. S., Willenborg, K., Foss, J. F., McGrath, J. J., and AbdulNour, B. S., 1997,
"Measurements of the Convective Heat Transfer Coefficient for a Two-Dimensional Wall Jet:
Uniform Temperature and Uniform Heat Flux Boundary Conditions", Proceedings of ASME
Heat Transfer Division, M.E. Ulucakli et al., Ed., HTD-Vol. 3, pp. 109-116.
[4] Thesues 3.1 Theory Manual.